Difference between revisions of "1990 AJHSME Problems/Problem 12"
5849206328x (talk | contribs) (Created page with '==Problem== There are twenty-four <math>4</math>-digit numbers that use each of the four digits <math>2</math>, <math>4</math>, <math>5</math>, and <math>7</math> exactly once. …') |
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[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] | ||
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Latest revision as of 00:05, 5 July 2013
Problem
There are twenty-four -digit numbers that use each of the four digits , , , and exactly once. Listed in numerical order from smallest to largest, the number in the position in the list is
Solution
For each choice of the thousands digit, there are numbers with that as the thousands digit. Thus, the six smallest are in the two thousands, the next six are in the four thousands, and then we need more numbers.
We can just list from here: .
See Also
1990 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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